Thinking Mathematically: Explore the quantitative dependencies of the acceleration upon the speed and the radius of curvature. Then answer the following questions. a. For the same speed, the acceleration of the object varies _____________ (directly, inversely) with the radius of curvature. b. For the same radius of curvature, the acceleration of the object varies _____________ (directly, inversely) with the speed of the object. c. As the speed of an object is doubled, the acceleration is __________________ (one-fourth, one-half, two times, four times) the original value. d. As the speed of an object is tripled, the acceleration is __________________ (one-third, one-ninth, three times, nine times) the original value. e. As the radius of the circle is doubled, the acceleration is __________________ (one-fourth, one-half, two times, four times) the original value. f. As the radius of the circle is tripled, the acceleration is __________________ (one-third, one-ninth, three times, nine times) the original value.

Answers

Answer 1

The expression for the centripetal acceleration allows to find the results for the questions are:

A) The acceleration varies INVERSELY with the radius of curvature.

B) The acceleration varies DIRECTLY with the speed.

C) The acceleration becomes four times greater.

D) The acceleration becomes nine times greater.

E) The acceleration is reduced to half.

F) The acceleration is reduced to a third.

In circular motion there must be an acceleration towards the center of the circle, it is called cenripetal acceleration, in this case all the energy supplied to the system is used to change the direction of the speed even when its magnitude remains constant.

        [tex]a_c = \frac{v^2}{r}[/tex]  

Where [tex]a_c[/tex] the centripetal acceleration, v is the speed and r the radius of curvature of the circle.

Now we can answer the questions about centripetal acceleration.

A) For the same speed, the acceleration varies INVERSELY with the radius of curvature.

B) For the same radius of curvature the acceleration varies DIRECTLY with the speed.

C) The speed is doubled

         v = 2 v₀

         [tex]a_c = \frac{(2v_o)^2 }{r}[/tex]  

         [tex]a_c = 4 \ \frac{v_o^2 }{r}[/tex]  

The acceleration becomes four times greater than the original value

D) The speed is tripled

         v = 3 v₀

         [tex]a_c = 9 \frac{ v_o^2}{r}[/tex]  

Acceleration becomes nine times greater than the original

E) the radius of curvature is doubled

        r = 2 r₀  

        [tex]a_c = \frac{v_o^2}{2 r_o }[/tex]  

        [tex]a_c = \frac{1}{2} a_o[/tex]  

Acceleration is reduced to half the original value

F) The radius of curvature is tripled

       r = 3 r₀

       [tex]a_c = \frac{v_o^2 }{3 r_o} \\ \\a_c = \frac{1}{3} a_o[/tex]  

       

The acceleration is reduced to a third of the initial one.

In conclusion using the expression for the centripetal acceleration we can find the answers for the questions are:

A) The acceleration varies INVERSELY with the radius of curvature.

B) The acceleration varies DIRECTLY with the speed.

C) The acceleration becomes four times greater.

D) The acceleration becomes nine times greater.

E) The acceleration is reduced to half.

F) The acceleration is reduced to a third.

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Related Questions

How can people reconcile technology with environmental preservation?​

Answers

1. Developing renewable energy technology

- Efficient energy storage and smarter grids .
- renewable and rechargeable batteries and fuel cell

2. Saving endangered wildlife

-smart collars for endangered species and reducing human - animal conflict
-Gene sequencing for detecting and researching on deadly animal diseases.

3. Adopting a smarter lifestyle

- smart homes that promote energy saving and green - living .
- electric cars which are three times more conventional vehicles .

Hope this helps :)

1. A small package is dropped from the Golden Gate Bridge. What is the velocity of the package
after it has fallen for 3.0 3?

Answers

The velocity of the package  after it has fallen for 3.0 s is 29.4 m/s

From the question,

A small package is dropped from the Golden Gate Bridge.

This means the initial velocity of the package is 0 m/s.

We are to calculate the velocity of the package  after it has fallen for 3.0 s.

From one of the equations of kinematics for objects falling freely,

We have that,

v = u + gt

Where

v is the final velocity

u is the initial velocity

g is the acceleration due to gravity

and t is time

To calculate the velocity of the package  after it has fallen for 3.0 s

That means, we will determine the value of v, at time t = 3.0 s

The parameters are

u = 0 m/s

g = 9.8 m/s²

t = 3.0 s

Putting these values into the equation

v = u + gt

We get

v = 0 + (9.8×3.0)

v = 0 + 29.4

v = 29.4 m/s

Hence, the velocity of the package  after it has fallen for 3.0 s is 29.4 m/s

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You throw a rock up into the air as hard as you can. It stays in the air a total of 6.0 s. What
was the velocity of the rock when you threw it?

Answers

Answer:

5.9 x 10

Explanation:

Câu 2: Một xe có khối lượng 20 tấn, chuyển động chậm dần đều dưới tác dụng của một lực 8000 N, vận tốc ban đầu của xe là 20 m/s. Gia tốc của xe là bai nhiêu?.

Answers

Answer:

?

Explanation:

Answer:

Explanation:yy

Which of the following statements is true?
a Penicillin is produced by fungal fermentation.
b
The effects of too much beer or wine can be
countered with antibiotics.
с
The deadly Death Cap mushroom can be treated
with penicillin.
d Antibiotics do not treat fungal diseases.

Answers

Answer:

a Penicillin is produced by fungal fermentation.

Explanation:

The industrial production of penicillin (PEN) occurs via fermentation using the filamentous fungus Penicillium chrysogenum

Penicillin G (benzylpenicillin) was first produced from a penicillium fungus that occurs in nature. The strain of fungus used today for the manufacture of penicillin G was created by genetic engineering to improve the yield in the manufacturing process.

An object starts from rest and uniformly accelerates at a rate of 1.25 m/s2 for 7.0 seconds.
(a) What is the object's displacement during this 7-second time period?
(b) What is the object's final velocity?
(c) How many seconds does it take the object to have a displacement of 22 meters?

Answers

Explanation:

Since its accelerating, the velocity vs time graph is linear

For displacement we need initial velocity (which is zero because it starts from rest) and final velocity (which is calculatee thro acceleration formula

A= (vf - vi)/t

a= vf-0/t

1.25=vf / 7

1.25*7=vf

8.75 = vf

Now for displacement plug all the values in

X = 1/2(vf-vi)/t formula

The displacement (x) is 30.625 m

For part 3, we know new displacement that is 22m , the final and initial velocities are the same so just plug in the values for same formula above

The answer is t = 5.02

Im pretty sure all the answers are correct

A ball moving 2 ft/s rolls off a table (on earth) that is 32 inches high. How long will it take the ball to hit the floor answer

Answers

Answer:When the ball rolls off the edge of the table, it will continue moving forward at 2.0 m/s until it hits the floor.

Explanation:This is what I would say is the answer bc I had to do reasearch on a lot of this for my work this year so if its not im veery sorry

Iron and nickel are examples of _______ materials

Content From May net

Answers

Answer:an iron-nickel alloy or nickel -iron alloy abbreviated FeNi or NiFe is a group of alloys consisting primarliy of the elemtns nickel and iron.

Explanation:

Answer:

Iron and nikel are example of "Metal" materials.

can anyone heelp me pls

Answers

Answer:

Lotion - Semisolid

Suspension - Liquid

Capsule - Solid

Lotion - Semisolid

Suspension - Liquid

Capsule - Solid



Please mark as brianliest answer.

Describe the shape of the earth besides round and tell me how it rotates​

Answers

Answer:

The Earth is in hydrostatic equilibrium pretty much. Which is to say that if it were entirely liquid it would still be the same shape ignoring minor differences like mountain ranges that are in any case indistinguishable on the large scale.

A spinning liquid sphere will flatten out somewhat at the axis poles and expand somewhat in its equatorial region and that’s the way the Earth is.

Hope it wirks

A 10 kg box initially at a speed of 10 m/s accelerates uniformly to a speed of 20 m/s in 2
seconds. Determine the
A. energy gained by the block

Answers

Answer:

What Um Sorry Where's The Answer?....

cách đổi ev sang kj/mol

Answers

Để chuyển đổi phép đo electronvolt thành phép đo kilojoule, hãy nhân năng lượng với tỷ lệ chuyển đổi. Năng lượng tính bằng kilojoules bằng electronvolt nhân với 1,6022E-22.

When adding vectors, what cannot change?
A. the vectors' length and direction
B. anything can change
C. only the vectors' length
D. only the vectors' direction
please help!!

Answers

Answer:

A

Explanation:

you cannot change the length and direction

number A is right I think

What is the magnitude of the electric field at a point 0.0075 m from a 0.0035
C charge?
Use E-
kq
and k - 9.00 x 10° N.m²/C2.
A. 1.9 x 1010 N
B. 4.2 x 10' N
O c. 5.6 x 1011 N
D. 5.5 x 1012 N

Answers

Explanation:

E = 9×10^9 × 0.0035 /(0.0075)²

= 9×10^9 × 3.5×10`³/(7.5×10`³)²

= 31.5×10^6 /(56.25 ×10^-6)

= 0.56 × 10^12

= 5.6 × 10^11 N/C (option C)

Someone help please i need to finish this

Answers

Answer:

4th answer

Explanation:

The gradient of a distance-time graph gives the speed.

gradient = distance / time = speed

Here, the gradient is a constant till 30s. So it has travelled at a constant speed. It means it had not accelarated till 30s. and has stopped moving at 30s.

What is the velocity of an object tht experiences 5.6m/s^2 and a radius of 3 meters?

Answers

The velocity of the object is 4.1 m/s. Recall that the centripetal acceleration is the acceleration of a body moving in a circular path.

Given that the centripetal acceleration is obtained using the formula;

ac = v^2/r

ac= centripetal acceleration

v = velocity

r = radius

v^2 = rac

v= √ rac

ac = 5.6m/s^2

r = 3 meters

Substituting values;

v = √3 × 5.6m/s^2

v = √16.8

v = 4.1 m/s

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Please Help!!! I have no idea :(


1. During an experiment in which you are investigating the acceleration changes due to force changes, what value must stay constant during these trials?

a. Force
b. Velocity
c. Acceleration
d. Mass

2. An animal is walking forward. There is an applied force from the animal of 25 N to the right, a frictional force of 18 N to the left, a force of gravity of 65 N down and the animal is being pushed up by the ground with 65 N. What best describes the motion of the animal?

a. The animal will move to the left due to an unbalanced force on the left
b. The animal will move to the right due to an unbalanced force on the right
c. The animal will move down due to an unbalanced force down
d. The animal will move up due to an unbalanced force upwards

3. Two rockets are being tested. Both rockets have the same mass. One rocket accelerates at a higher rate than another rocket. What could be true about the difference between the rockets?

a. One rocket has more fuel than the other
b. One rocket is more streamlined than the other
c. One rocket engine produces more force than the other
d. One rocket is more badly designed than the other

4. According to Newton's Third Law, if a sledgehammer hits a wall with a force of 1000 N, how much force does the wall hit the sledgehammer?

a. 0 N
b. 500 N
c. 1000 N
d. - 1000 N

Answers

Answer:

1. A. Force

2.

3. B. or C.

4. 1,000 N as well

Explanation:

1. Force is mass multiplied by acceleration. if force and mass stay constant, then according to that equation, the acceleration stays constant as well.

I couldn't figure out what number 2 is though. Sorry.

The value which must stay constant during these trial is:

A. Force

The best description of the motion of the animal is:

B. The animal will move to the right due to an unbalanced force on the right  

The thing which could be true about the difference between the rockets is:

C. One rocket engine produces more force than the other

The amount of force which the wall hits the sledgehammer is:

C. 1000 N

Force is simply defined as the mass of a body which is multiplied by the acceleration and according to the laws of physics, if there is a constant in the mass and force, then the acceleration would also remain constant.

Read more here:

https://brainly.com/question/24557735

Does static electricity light our homes? True or false

Answers

Answer:

No, false.

Explanation:

You may use it to power a light bulb if you desired. The reason it isn't is because it's inconsistent not predictable.

The static electricity light our homes. This statement is false.

What is static electricity?

When two objects are rubbed, they get charged by friction present into it. Object can also be charged by induction.

The charge gets accumulated on them, due to which spark occurs.

This spark cannot light our homes. As, this has very less magnitude and no continuous flow. There is no complete circuit to get the continuous flow of electricity.

Thus, static electricity can't light our homes.

Learn more about  static electricity.

https://brainly.com/question/12791045

#SPJ2

Which of the following is NOT a way that a U-235 atom could fission?

Answers

Answer: A.

just did it

Explanation:

What does it mean when my teacher asks me to "use appropriate figures"?

Answers

Answer:

In science

Explanation:

When a teacher tells you so use the appropriate figures. He/she means to use the proper amount of Sig figs or Significant digits.

Example: Is the picture

In the example the answer is 7.31 because you have to take the less number of significant digits

Answer:

figures that are relevant or suitable for the question asked

The following question has two parts. First, answer part A. Then, answer part B.

Part A:
Why did the author most likely choose the title “Breaking Barriers” for this text?

A.
to show that Elizabeth worked hard to make people like her

B.
to show that Elizabeth accomplished things never done before

C.
to show that Elizabeth proved to be smarter than those around her

D.
to show that Elizabeth tried to show she was the better than other doctors

Part B:
Which sentences from the text best support your answer in part A? Select two options.

A.
“Elizabeth loved learning, and she developed a passion for reading.”

B.
“When Elizabeth was 11 years old, her family moved to America.”

C.
“When she was just 16, she became a teacher.”

D.
“Finally, the Geneva Medical College in New York accepted her as a student.”

E.
“When people in town ignored the woman with the strange ambition, Elizabeth treated them in a polite, quiet manner.”

F.
“She became the first woman in the country to obtain a medical degree.”

Answers

Answer:

for part A the answer is D and for part B the answer is F

PLEASE HELP ASAP WILL GIVE BRAINLIEST ​

Answers

Explanation

(m) is measured in kilograms (kg)

(F) is measured in newtons (N)

acceleration (a) is measured in metres per second squared (m/s²)

Q1) ~mass (m) is measured in kilograms (kg) 

Q2)~acceleration (a) is measured in metres per second squared (m/s²)

Q3)~force (F) is measured in newtons (N)

Hope this helped you- have a good day bro cya)

Sharing thoughts on a peer's story is similar to... a.being a teacher b.listening to a lesson c.editing a story d.a collaborative discussion

Answers

Answer:

D

Explanation:

when sharing ideas, you are being collaborative

What force is required to accelerate a 1000-kilogram car at 6 m/s??

Answers

Answer:

Hence, Force (F) is 4000 Newtons.

Explanation:

ɢɪᴠᴇɴ :-

Mass (m) = 1000 kg

Acceleration (a) = 4 m/s²

ᴛᴏ Find:-

Force (F)

solution :-

We know that,

Force = mass × acceleration

➮ F = ma

➮ F = 1000 × 4

➮ F = 4000 N

Hence,

Force (F) is 4000 Newtons

(Hope this helps can I pls have brainlist (crown)☺️)

If you traveled 50m/s for 60 seconds, how far did you travel? Remember speed=distance/time
Question options:


300 m/s



500 m/s



3,000 m/s



300 km/h

for some reason my question got removed-_-

Answers

the answer is 3,000 m/s

Ano ang mangyayari kung hindi mo gagamitin ang iyong talento?​

Answers

Answer:

mas lalo kang tinatamaran magaral

Motion maps for two objects, Y & Z, are shown.

How many seconds does Object Z start before Object Y?
- 2
- 3
- 4
- 5

Answers

Answer: it’s 3 seconds

Explanation:

Answer:

B

Explanation:

3 seconds, hope it helps

Name the type of joint present in skull.​

Answers

Answer:

Sutures are nonmoving joints that connect bones of the skull

Explanation:

These joints have serrated edges that lock together with fibers of connective tissue.

Answer:

Immovable fibrous joints are present in our skull

Explanation:

brainliest plz

Speed depends on how far something travels and

Answers

Answer:

Speed depends on how far something is travelling and the time taken for the object to travel that distance

Explanation:

(In reference to the speed formula)  Speed=[tex]\frac{Distance(m)}{Time(m/s)}[/tex]

Definition of speed:

Speed is the magnitude (unit) of the rate at which an object is moving.

(pls do correct me if I have any mistakes it makes a big difference to help each other out!)

Two students were pushing a heavy sofa. One student pushed with a force of 200.0 N to the right, while the other pushed with a force of 150.0 N to the right. The floor exerted a frictional force of 100.0 N. If the sofa's mass is 91.0 kg, what is its acceleration? Round your answer to three significant figures.

Answers

Answer:

Explanation:

F = ma

a = F/m

a = (200.0 + 150.0 - 100.0) / 91.0

a = 250.0/91.0

a = 2.7472527...

a = 2.75 m/s²

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